Question

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m. The answer is 61 i want to see the solution to this problem

Answer 1

Solution-

At x = 4 the field m will be the sum of the electric fields produced by a series of point charges between x = 0 and x = 3 m.

Each infinitesimal length of the line charge has a charge of dq = D dx,

Here D is the linear charge density. Each of these infinitesimal lengths can be treated as a point charge with charge dq = D dx.

The electric field at a distance x from a point charge is dE = k*dq/x^2, = k*D*dx/x^2

here k is Coulomb's constant = 8.99*10^9 (N*m^2)/(C^2)

The field at x = 4 m is then given as
E = Integral from x = (4-3) to 4 of {k*D/x^2 dx}

E = k*D*Integral from x = 1 to 4 of {dx/x^2}

E = -k*D*(1/4m - 1/1m)

Putting the values for k and D, we get

E = 60.68 N/C this is approx. equal to 61